where convergence takes place in \(L^2(\mu )\) . It is known (see [1]}) that the convergence in (REF )
cannot be strengthened to pointwise convergence for every \(x\in X\) . We do not know if under the stated assumptions the convergence in (REF ) can be strengthened to pointwise convergence for \(m_X\) -almost every \(x\in X\)  and all \(f_1,\ldots , f_\ell \in C(X)\) .
